On-off frequency-shift keying for wideband fading channels

r Eb P/N0 = − → log 2 = −1.59 dB. N0 C B→∞ e
(1)
This minimum bit energy (1) can be approached by pulseposition modulation with vanishing duty cycle [3] or by M ary orthogonal signaling as M becomes large [4]. In the presence of unknown fading, Jacobs [5] and Pierce [6] have noted that M -ary orthogonal signaling obtained by frequency-shift keying (FSK) modulation can still approach the limit in (1) for large values of M . Gallager [7, Section 8.6] also demonstrated that over fading channels M -ary orthogonal FSK signaling with vanishing duty cycle approaches the infinite bandwidth capacity of unfaded Gaussian channels as M → ∞, thereby achieving (1). The result that the infinite bandwidth capacity of fading channels is the same as that of unfaded Gaussian channels is also noted by Kennedy [8]. Telatar and Tse [9] considered a more general fading channel model that consists of a finite number of time-varying paths and showed that the infinite bandwidth capacity of this channel is again approached by using peaky FSK signaling. Luo
Received 9 March 2005; Revised 20 August 2005; Accepted 15 September 2005 Recommended for Publication by Richard Kozick M -ary on-off frequency-shift keying (OOFSK) is a digital modulation format in which M -ary FSK signaling is overlaid on on/off keying. This paper investigates the potential of this modulation format in the context of wideband fading channels. First, it is assumed that the receiver uses energy detection for the reception of OOFSK signals. Capacity expressions are obtained for the cases in which the receiver has perfect and imperfect fading side information. Power efficiency is investigated when the transmitter is subject to a peak-to-average power ratio (PAR) limitation or a peak power limitation. It is shown that under a PAR limitation, it is extremely power inefficient to operate in the very-low-SNR regime. On the other hand, if there is only a peak power limitation, it is demonstrated that power efficiency improves as one operates with smaller SNR and vanishing duty factor. Also studied are the capacity improvements that accrue when the receiver can track phase shifts in the channel or if the received signal has a specular component. To take advantage of those features, the phase of the modulation is also allowed to carry information. Copyright © 2006 M. C. Gursoy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
A wide range of digital communication systems in wireless, deep space, and sensor networks operate in the low-power regime where power consumption rather than bandwidth is the limiting factor. For such systems, power-efficient transmission schemes are required for effective use of scarce energy resources. For example, in sensor networks [1], nodes that are densely deployed in a region may be equipped with only a limited power source and in some cases replenishment of these resources may not be possible. Therefore, energyefficient operation is vital in these systems. Recently, there has also been much interest in ultra-wideband systems in which low-power pulses of very short duration are used for communication over short distances. These wideband pulses must satisfy strict peak power requirements in order not to interfere with existing systems. The power efficiency of a communication system can be measured by the energy required for reliable communication of one bit. When communicating at rate R bps with power P , the transmitted energy per bit is Eb = P/R. Since the maximum rate is given by the channel capacity, C , the least amount of bit energy required for reliable communication is Eb = P/C . In [2], Shannon showed that the capacity of an ideal bandlimited additive white Gaussian noise channel is C = B log2 (1 + P/BN0 ) bps, where P is the received
Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2006, Article ID 98564, Pages 1–15 DOI 10.1155/WCN/2006/98564
power, B is the channel bandwidth, and N0 is the one-sided noise spectral level. As the bandwidth grows to infinity, the capacity monotonically increases to (P/N0 ) log2 e bps, therefore decreasing the required received bit energy normalized to the noise power toon Wireless Communications and Networking signaling has average power P , and peak power P/ ν. We assume that the transmitted signal undergoes stationary and ergodic fading and that the delay spread of the fading is much less than the symbol duration. Under these assumptions, the fading has a multiplicative effect on the transmitted signal and the received signal can be modeled as follows: r (t ) = h(t )sXk t − (k − 1)T + n(t ), (k − 1)T ≤ t ≤ kT , for k = 1, 2, . . . , (3)